反射布朗运动平稳分布的深度学习方法
Deep Learning Method for Stationary Distribution of Reflected Brownian Motion
AI总结：
研究反射布朗运动平稳分布，基于基本伴随关系开发深度学习方法学习其拉普拉斯变换，精心设计框架各部分，在已知尾概率的实例上评估，结果近乎完美，有望成为分析随机系统的通用工具。
摘要：
反射布朗运动（RBM）的平稳分布在高维随机系统分析中起重要作用，但仅在少数特殊情况下有闭式解。计算重要性能指标（如尾概率）更难处理，尽管其具有实际相关性。本文基于基本伴随关系（BAR）开发了一种深度学习方法，能准确高效地学习高维RBM的拉普拉斯变换。该框架结合了损失函数、训练数据采样程序和神经网络架构的精心设计。在已知真实尾概率的RBM实例上评估，结果显示在高维设置中预测近乎完美，凸显其作为分析随机系统通用工具的潜力。代码可在指定网址获取。
英文摘要：
The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases. Computing important performance metrics, such as tail probabilities, is even more intractable, despite their practical relevance. In this paper, we develop a deep learning approach that accurately and efficiently learns the Laplace transform of high-dimensional RBMs based on the basic adjoint relationship (BAR). Our framework combines a careful design of the loss function, training data sampling procedure, and neural network architecture. We evaluate the proposed method on RBM instances with known ground-truth tail probabilities and demonstrate near-perfect prediction in high-dimensional settings, highlighting its potential as a general tool for analyzing stochastic systems beyond analytically tractable regimes. Our code can be found at https://github.com/zhangz73/NN4MGF.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
